A graph is called (matching-)immune if it has no edge cut that is also a matching. Farley and Proskurowski proved that for all immune graphs G=(V,E) , |E|≥⌈3(|V|-1)/2⌉ , and constructed a large class of immune graphs that attain this lower bound for every value of |V(G)| , called ABC graphs. They conjectured that every immune graph that attains this lower bound is an ABC graph. We present a proof of this conjecture.